How to connect two different Textures on the same faces with a transparent background?
You should not add shaders in this situation. If you add shaders, one reflects all the light according to it's properties, but then everything that another one reflects according to its properties gets added to the result. In reality, that does not happen with a material that only has a few different colors. You should use the Mix Shader node in this case, or if it is only a color, you should only mix the color of the shader, instead of a copy of that exact same shader with a different color. 

How you mix everything depends on what you want to achieve. 

It would make a whole lot more sense to have the triangles on the right color and in one texture in the first place, but let's just say only for learning purposes the task is to add two triangles one on top another and for some unknown, but very important reason they need to be on black backgrounds in the textures, but the color of the material needs to be white. 

You would need to make a black and white mask for each of the triangles to separate them from the background. Let's use Math node set to Greater Than mode with a small value for this, so we make all brighter than the small value colors show white. Both triangles need to be mixed on top of your desired color using Mix RGB node. Note that one Mix RGB node has white in it that is the new white background:



Edit:
I just noticed you have one shader with different metallic value. It would make more sense to have the colors in one texture and just a grey-scale map for that single metallic property that is different.

There is nothing mysterious about using grey-scale map for something. Think of it like using a single value, like you are now, just for different parts of the material defined by the texture file. You have metallic value 0 and 1.0 so you only need completely black and completely white in the map. What will be the most convenient way for you to make it depends on how you make the textures. If it is in some external painting software like Krita or Photoshop, or Gimp, you would just make sure you make one image with white instead of the yellow line and black instead of everything else. Then you would just drag and drop the image into the nodes of the material and plug it into the Metallic input.